A Professor of Accounting Wanted to Develop a Multiple Regression $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$

question 43

Essay

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
where
y
= fourth-year accounting course mark (out of 100). $x _ { 1 }$ = GPA in first three years (range 0 to 12). $x _ { 2 }$ = 1 if student's major is accounting.
= 0 if not. $X _ { 3 }$ = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS $y =$ $$9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$$ . $$\begin{array} { | c | r r c | } \hline \text { Predictor } & \text { Coef } & \text { SDev } & T \\\hline \text { Constant } & 9.14 & 7.10 & 1.287 \\x _ { 1 } & 6.73 & 1.91 & 3.524 \\x _ { 2 } & 10.42 & 4.16 & 2.505 \\x _ { 3 } & 5.16 & 3.93 & 1.313 \\\hline\end{array}$$ S = 15.0 R-Sq = 44.2%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r r r r | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \\\text { Error } & 96 & 21553 & 224.510 & \\\hline \text { Total } & 99 & 38651 & & \\\hline\end{array}\end{array}$$ Do these results allow us to conclude at the 1% significance level that grade point average in the first three years is linearly related to fourth-year accounting course mark?

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Definitions:

Behaviorism

A school of psychology that focuses on observable behaviors as the subject matter and disregards internal processes like thinking.

Belongingness Needs

A fundamental human need to form and maintain strong, stable interpersonal relationships.

Esteem Needs

These are psychological requirements for respect, self-esteem, and recognition, forming a part of Maslow's hierarchy of needs.

Psychoanalysis

A set of theories and therapeutic techniques related to the study of the unconscious mind, developed by Sigmund Freud, that aims to treat mental disorders.